Page 1 1 Answers & Solutions for for for for for JEE (Advanced)2018 Time : 3 hrs. Max. Marks: 180 PAPER  2 PARTI : PHYSICS SECTION  1 (Maximum Marks : 24) ? This section contains SIX (06) questions. ? Each question has FOUR options for correct answer(s). ONE OR MORE THAN ONE of these four option(s) is (are) correct option(s). ? For each question, choose the correct option(s) to answer the question. ? Answer to each question will be evaluated according to the following marking scheme: Full Marks : +4 If only (all) the correct option(s) is (are) chosen. Partial Marks : +3 If all the four options are correct but ONLY three options are chosen. Partial Marks : +2 If three or more options are correct but ONLY two options are chosen, both of which are correct options. Partial Marks : +1 If two or more options are correct but ONLY one option is chosen and it is a correct option. Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered). Negative Marks : –2 In all other cases. For Example: If first, third and fourth are the ONLY three correct options for a question with second option being an incorrect option; selecting only all the three correct options will result in +4 marks. Selecting only two of the three correct options (e.g. the first and fourth options), without selecting any incorrect option (second option in this case), will result in +2 marks. Selecting only one of the three correct options (either first or third or fourth option), without selecting any incorrect option (second option in this case), will result in +1 marks. Selecting any incorrect option(s) (second option in this case), with or without selection of any correct option(s) will result in –2 marks. Page 2 1 Answers & Solutions for for for for for JEE (Advanced)2018 Time : 3 hrs. Max. Marks: 180 PAPER  2 PARTI : PHYSICS SECTION  1 (Maximum Marks : 24) ? This section contains SIX (06) questions. ? Each question has FOUR options for correct answer(s). ONE OR MORE THAN ONE of these four option(s) is (are) correct option(s). ? For each question, choose the correct option(s) to answer the question. ? Answer to each question will be evaluated according to the following marking scheme: Full Marks : +4 If only (all) the correct option(s) is (are) chosen. Partial Marks : +3 If all the four options are correct but ONLY three options are chosen. Partial Marks : +2 If three or more options are correct but ONLY two options are chosen, both of which are correct options. Partial Marks : +1 If two or more options are correct but ONLY one option is chosen and it is a correct option. Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered). Negative Marks : –2 In all other cases. For Example: If first, third and fourth are the ONLY three correct options for a question with second option being an incorrect option; selecting only all the three correct options will result in +4 marks. Selecting only two of the three correct options (e.g. the first and fourth options), without selecting any incorrect option (second option in this case), will result in +2 marks. Selecting only one of the three correct options (either first or third or fourth option), without selecting any incorrect option (second option in this case), will result in +1 marks. Selecting any incorrect option(s) (second option in this case), with or without selection of any correct option(s) will result in –2 marks. 2 JEE (ADVANCED)2018 (PAPER2) 1. A particle of mass m is initially at rest at the origin. It is subjected to a force and starts moving along the xaxis. Its kinetic energy K changes with time as dK/dt = ? ? ? ? ?t, where ? ? ? ? ? is a positive constant of appropriate dimensions. Which of the following statements is (are) true? (A) The force applied on the particle is constant (B) The speed of the particle is proportional to time (C) The distance of the particle from the origin increases linearly with time (D) The force is conservative Answer (A, B, D) Sol. ? ? ? 2 1dK dv Kmv mv 2dt dt given, ?? ? ?? dK dv tmv t dt dt ? ?? ? ? ? ?? vt 22 00 vt vdv tdt m2m2 ? ? ?vt m ? ? ?? dv a dt m ??? ? Fma m constant ?? ? ? ? 2 dS t tS dt m m 2 2. Consider a thin square plate floating on a viscous liquid in a large tank. The height h of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity u 0 . Which of the following statements is (are) true? (A) The resistive force of liquid on the plate is inversely proportional to h (B) The resistive force of liquid on the plate is independent of the area of the plate (C) The tangential (shear) stress on the floor of the tank increases with u 0 (D) The tangential (shear) stress on the plate varies linearly with the viscosity ? ? ? ? ? of the liquid Answer (A, C, D) Sol. u 0 F v A Plate ?? ?? ?? ?? v dv FA dz Since height h of the liquid in tank is very small ? ?? ? ?? ?? ? ?? 0 u dv v dz z h ?? ?? ?? ?? 0 v u F()A h ?? ?? ? ?? ?? ?? vv0v v 1 F,Fu,FA,F h Page 3 1 Answers & Solutions for for for for for JEE (Advanced)2018 Time : 3 hrs. Max. Marks: 180 PAPER  2 PARTI : PHYSICS SECTION  1 (Maximum Marks : 24) ? This section contains SIX (06) questions. ? Each question has FOUR options for correct answer(s). ONE OR MORE THAN ONE of these four option(s) is (are) correct option(s). ? For each question, choose the correct option(s) to answer the question. ? Answer to each question will be evaluated according to the following marking scheme: Full Marks : +4 If only (all) the correct option(s) is (are) chosen. Partial Marks : +3 If all the four options are correct but ONLY three options are chosen. Partial Marks : +2 If three or more options are correct but ONLY two options are chosen, both of which are correct options. Partial Marks : +1 If two or more options are correct but ONLY one option is chosen and it is a correct option. Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered). Negative Marks : –2 In all other cases. For Example: If first, third and fourth are the ONLY three correct options for a question with second option being an incorrect option; selecting only all the three correct options will result in +4 marks. Selecting only two of the three correct options (e.g. the first and fourth options), without selecting any incorrect option (second option in this case), will result in +2 marks. Selecting only one of the three correct options (either first or third or fourth option), without selecting any incorrect option (second option in this case), will result in +1 marks. Selecting any incorrect option(s) (second option in this case), with or without selection of any correct option(s) will result in –2 marks. 2 JEE (ADVANCED)2018 (PAPER2) 1. A particle of mass m is initially at rest at the origin. It is subjected to a force and starts moving along the xaxis. Its kinetic energy K changes with time as dK/dt = ? ? ? ? ?t, where ? ? ? ? ? is a positive constant of appropriate dimensions. Which of the following statements is (are) true? (A) The force applied on the particle is constant (B) The speed of the particle is proportional to time (C) The distance of the particle from the origin increases linearly with time (D) The force is conservative Answer (A, B, D) Sol. ? ? ? 2 1dK dv Kmv mv 2dt dt given, ?? ? ?? dK dv tmv t dt dt ? ?? ? ? ? ?? vt 22 00 vt vdv tdt m2m2 ? ? ?vt m ? ? ?? dv a dt m ??? ? Fma m constant ?? ? ? ? 2 dS t tS dt m m 2 2. Consider a thin square plate floating on a viscous liquid in a large tank. The height h of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity u 0 . Which of the following statements is (are) true? (A) The resistive force of liquid on the plate is inversely proportional to h (B) The resistive force of liquid on the plate is independent of the area of the plate (C) The tangential (shear) stress on the floor of the tank increases with u 0 (D) The tangential (shear) stress on the plate varies linearly with the viscosity ? ? ? ? ? of the liquid Answer (A, C, D) Sol. u 0 F v A Plate ?? ?? ?? ?? v dv FA dz Since height h of the liquid in tank is very small ? ?? ? ?? ?? ? ?? 0 u dv v dz z h ?? ?? ?? ?? 0 v u F()A h ?? ?? ? ?? ?? ?? vv0v v 1 F,Fu,FA,F h 3 JEE (ADVANCED)2018 (PAPER2) 3. An infinitely long thin nonconducting wire is parallel to the zaxis and carries a uniform line charge density ? ? ? ? ?. It pierces a thin nonconducting spherical shell of radius R in such a way that the arc PQ subtends an angle 120° at the centre O of the spherical shell, as shown in the figure. The permittivity of free space is ? ? ? ? ? 0 . Which of the following statements is (are) true? ? P R O Q 120° z (A) The electric flux through the shell is 0 3R ? ? (B) The zcomponent of the electric field is zero at all the points on the surface of the shell (C) The electric flux through the shell is 0 2R ? ? (D) The electric field is normal to the surface of the shell at all points Answer (A, B) Sol. PQ = (2) R sin 60° ? P R O Q 120° z R ?? 3 (2R) 3R 2 ?? ?? enclosed Q3R ?? We have ?? ? enclosed 0 q ? ?? ? ?? ?? ?? ? ?? 0 3R Also electric filed is perpendicular to wire so Zcomponent will be zero. Page 4 1 Answers & Solutions for for for for for JEE (Advanced)2018 Time : 3 hrs. Max. Marks: 180 PAPER  2 PARTI : PHYSICS SECTION  1 (Maximum Marks : 24) ? This section contains SIX (06) questions. ? Each question has FOUR options for correct answer(s). ONE OR MORE THAN ONE of these four option(s) is (are) correct option(s). ? For each question, choose the correct option(s) to answer the question. ? Answer to each question will be evaluated according to the following marking scheme: Full Marks : +4 If only (all) the correct option(s) is (are) chosen. Partial Marks : +3 If all the four options are correct but ONLY three options are chosen. Partial Marks : +2 If three or more options are correct but ONLY two options are chosen, both of which are correct options. Partial Marks : +1 If two or more options are correct but ONLY one option is chosen and it is a correct option. Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered). Negative Marks : –2 In all other cases. For Example: If first, third and fourth are the ONLY three correct options for a question with second option being an incorrect option; selecting only all the three correct options will result in +4 marks. Selecting only two of the three correct options (e.g. the first and fourth options), without selecting any incorrect option (second option in this case), will result in +2 marks. Selecting only one of the three correct options (either first or third or fourth option), without selecting any incorrect option (second option in this case), will result in +1 marks. Selecting any incorrect option(s) (second option in this case), with or without selection of any correct option(s) will result in –2 marks. 2 JEE (ADVANCED)2018 (PAPER2) 1. A particle of mass m is initially at rest at the origin. It is subjected to a force and starts moving along the xaxis. Its kinetic energy K changes with time as dK/dt = ? ? ? ? ?t, where ? ? ? ? ? is a positive constant of appropriate dimensions. Which of the following statements is (are) true? (A) The force applied on the particle is constant (B) The speed of the particle is proportional to time (C) The distance of the particle from the origin increases linearly with time (D) The force is conservative Answer (A, B, D) Sol. ? ? ? 2 1dK dv Kmv mv 2dt dt given, ?? ? ?? dK dv tmv t dt dt ? ?? ? ? ? ?? vt 22 00 vt vdv tdt m2m2 ? ? ?vt m ? ? ?? dv a dt m ??? ? Fma m constant ?? ? ? ? 2 dS t tS dt m m 2 2. Consider a thin square plate floating on a viscous liquid in a large tank. The height h of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity u 0 . Which of the following statements is (are) true? (A) The resistive force of liquid on the plate is inversely proportional to h (B) The resistive force of liquid on the plate is independent of the area of the plate (C) The tangential (shear) stress on the floor of the tank increases with u 0 (D) The tangential (shear) stress on the plate varies linearly with the viscosity ? ? ? ? ? of the liquid Answer (A, C, D) Sol. u 0 F v A Plate ?? ?? ?? ?? v dv FA dz Since height h of the liquid in tank is very small ? ?? ? ?? ?? ? ?? 0 u dv v dz z h ?? ?? ?? ?? 0 v u F()A h ?? ?? ? ?? ?? ?? vv0v v 1 F,Fu,FA,F h 3 JEE (ADVANCED)2018 (PAPER2) 3. An infinitely long thin nonconducting wire is parallel to the zaxis and carries a uniform line charge density ? ? ? ? ?. It pierces a thin nonconducting spherical shell of radius R in such a way that the arc PQ subtends an angle 120° at the centre O of the spherical shell, as shown in the figure. The permittivity of free space is ? ? ? ? ? 0 . Which of the following statements is (are) true? ? P R O Q 120° z (A) The electric flux through the shell is 0 3R ? ? (B) The zcomponent of the electric field is zero at all the points on the surface of the shell (C) The electric flux through the shell is 0 2R ? ? (D) The electric field is normal to the surface of the shell at all points Answer (A, B) Sol. PQ = (2) R sin 60° ? P R O Q 120° z R ?? 3 (2R) 3R 2 ?? ?? enclosed Q3R ?? We have ?? ? enclosed 0 q ? ?? ? ?? ?? ?? ? ?? 0 3R Also electric filed is perpendicular to wire so Zcomponent will be zero. 4 JEE (ADVANCED)2018 (PAPER2) 4. A wire is bent in the shape of a right angled triangle and is placed in front of a concave mirror of focal length f, as shown in the figure. Which of the figures shown in the four options qualitatively represent( s) the shape of the image of the bent wire? (These figures are not to scale). 45° f f 2 (A) ? ? > 45° (B) ? (C) ? 0 < < 45° ?? (D) ? Answer (D) Sol. Image of point A f/2 B A Q (f – x) x C P O ?? ? ? ? ?? ? ?? ?? 11 1 vf f vf 2 ? ?? ? ? ? AB AB I f I2AB f AB 2 For Height of PQ ? ?? ??? ? ? ?? ? ? 11 1 1 1 1 f(fx) v v(fx) f v (fx) f x ? ? ?? ?? ? ?? ?? ?? PQ I f(fx) f PQ x{(fx)} x ? PQ f f2(AB)x IPQ xx f ??? ? ?? ??? ? ??? ? 2(AB)x PQ f ?? ? ?? ?? ? I PQ = 2AB (Size of image is independent of x. So, final image will be of same height terminating at infinity) Page 5 1 Answers & Solutions for for for for for JEE (Advanced)2018 Time : 3 hrs. Max. Marks: 180 PAPER  2 PARTI : PHYSICS SECTION  1 (Maximum Marks : 24) ? This section contains SIX (06) questions. ? Each question has FOUR options for correct answer(s). ONE OR MORE THAN ONE of these four option(s) is (are) correct option(s). ? For each question, choose the correct option(s) to answer the question. ? Answer to each question will be evaluated according to the following marking scheme: Full Marks : +4 If only (all) the correct option(s) is (are) chosen. Partial Marks : +3 If all the four options are correct but ONLY three options are chosen. Partial Marks : +2 If three or more options are correct but ONLY two options are chosen, both of which are correct options. Partial Marks : +1 If two or more options are correct but ONLY one option is chosen and it is a correct option. Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered). Negative Marks : –2 In all other cases. For Example: If first, third and fourth are the ONLY three correct options for a question with second option being an incorrect option; selecting only all the three correct options will result in +4 marks. Selecting only two of the three correct options (e.g. the first and fourth options), without selecting any incorrect option (second option in this case), will result in +2 marks. Selecting only one of the three correct options (either first or third or fourth option), without selecting any incorrect option (second option in this case), will result in +1 marks. Selecting any incorrect option(s) (second option in this case), with or without selection of any correct option(s) will result in –2 marks. 2 JEE (ADVANCED)2018 (PAPER2) 1. A particle of mass m is initially at rest at the origin. It is subjected to a force and starts moving along the xaxis. Its kinetic energy K changes with time as dK/dt = ? ? ? ? ?t, where ? ? ? ? ? is a positive constant of appropriate dimensions. Which of the following statements is (are) true? (A) The force applied on the particle is constant (B) The speed of the particle is proportional to time (C) The distance of the particle from the origin increases linearly with time (D) The force is conservative Answer (A, B, D) Sol. ? ? ? 2 1dK dv Kmv mv 2dt dt given, ?? ? ?? dK dv tmv t dt dt ? ?? ? ? ? ?? vt 22 00 vt vdv tdt m2m2 ? ? ?vt m ? ? ?? dv a dt m ??? ? Fma m constant ?? ? ? ? 2 dS t tS dt m m 2 2. Consider a thin square plate floating on a viscous liquid in a large tank. The height h of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity u 0 . Which of the following statements is (are) true? (A) The resistive force of liquid on the plate is inversely proportional to h (B) The resistive force of liquid on the plate is independent of the area of the plate (C) The tangential (shear) stress on the floor of the tank increases with u 0 (D) The tangential (shear) stress on the plate varies linearly with the viscosity ? ? ? ? ? of the liquid Answer (A, C, D) Sol. u 0 F v A Plate ?? ?? ?? ?? v dv FA dz Since height h of the liquid in tank is very small ? ?? ? ?? ?? ? ?? 0 u dv v dz z h ?? ?? ?? ?? 0 v u F()A h ?? ?? ? ?? ?? ?? vv0v v 1 F,Fu,FA,F h 3 JEE (ADVANCED)2018 (PAPER2) 3. An infinitely long thin nonconducting wire is parallel to the zaxis and carries a uniform line charge density ? ? ? ? ?. It pierces a thin nonconducting spherical shell of radius R in such a way that the arc PQ subtends an angle 120° at the centre O of the spherical shell, as shown in the figure. The permittivity of free space is ? ? ? ? ? 0 . Which of the following statements is (are) true? ? P R O Q 120° z (A) The electric flux through the shell is 0 3R ? ? (B) The zcomponent of the electric field is zero at all the points on the surface of the shell (C) The electric flux through the shell is 0 2R ? ? (D) The electric field is normal to the surface of the shell at all points Answer (A, B) Sol. PQ = (2) R sin 60° ? P R O Q 120° z R ?? 3 (2R) 3R 2 ?? ?? enclosed Q3R ?? We have ?? ? enclosed 0 q ? ?? ? ?? ?? ?? ? ?? 0 3R Also electric filed is perpendicular to wire so Zcomponent will be zero. 4 JEE (ADVANCED)2018 (PAPER2) 4. A wire is bent in the shape of a right angled triangle and is placed in front of a concave mirror of focal length f, as shown in the figure. Which of the figures shown in the four options qualitatively represent( s) the shape of the image of the bent wire? (These figures are not to scale). 45° f f 2 (A) ? ? > 45° (B) ? (C) ? 0 < < 45° ?? (D) ? Answer (D) Sol. Image of point A f/2 B A Q (f – x) x C P O ?? ? ? ? ?? ? ?? ?? 11 1 vf f vf 2 ? ?? ? ? ? AB AB I f I2AB f AB 2 For Height of PQ ? ?? ??? ? ? ?? ? ? 11 1 1 1 1 f(fx) v v(fx) f v (fx) f x ? ? ?? ?? ? ?? ?? ?? PQ I f(fx) f PQ x{(fx)} x ? PQ f f2(AB)x IPQ xx f ??? ? ?? ??? ? ??? ? 2(AB)x PQ f ?? ? ?? ?? ? I PQ = 2AB (Size of image is independent of x. So, final image will be of same height terminating at infinity) 5 JEE (ADVANCED)2018 (PAPER2) 5. In a radioactive decay chain, 232 90 Th nucleus decays to 212 82 Pb nucleus. Let N ? and N ? be the number of ? ? ? ? ? and ? ? ? ? ? – particles, respectively, emitted in this decay process. Which of the following statements is (are) true? (A) ? ? N5 (B) ? ? N6 (C) ? ? N2 (D) ? ? N4 Answer (A, C) Sol. ?? ? ? ?? ? ? ? Decay AA4 ZZ2 XY Decay AA ZZ11 XX ? ?? ? ????? ? ?? ? 232 212 90 82 Th Pb No. of ?particles emitted ? ?? 232 212 5 4 Since Z decreases by (90 – 82) = 8 only Hence no. of ? – decay = 2 6. In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency 500 Hz is used. The length of the air column is varied by changing the level of water in the resonance tube. Two successive resonances are heard at air columns of length 50.7 cm and 83.9 cm. Which of the following statements is (are) true? (A) The speed of sound determined from this experiment is 332 ms –1 (B) The end correction in this experiment is 0.9 cm (C) The wavelength of the sound wave is 66.4 cm (D) The resonance at 50.7 cm corresponds to the fundamental harmonic Answer (A, B, C) Sol. ? ?? (2n–1) 50.7 e 4 ?? 2(n 1)–1 83.9 e 4 ? ?? ? ? ? ?? 83.9–50.7 33.2cm 2 ?? = 66.4 cm v = ?f = 66.4 × 500 × 10 –2 m/s = 332 m/s For, n = 2, e = – 0.9 cmRead More
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